My research focuses on social networks. Social networks, at least as I deal with them, are representations of how people (or organizations, or animals) perceive or interact with each other. These representations can take the form of visualizations (see below for an example) matrices, or lists of who is connected to who. How you decide to format your representation of a network depends on what you are trying to learn, how many people and relationships are in the network, and what kind of relationships you are interested in. In this blog post we will just be looking at network visualizations.

Wayne Zachary was not actually in the karate club, but he kept track of who in the club hung out with each other doing non-karate activities for three years. So in the above representation of the network, you can see that the person labelled 25 interacted with the person labelled 32 outside of the karate club. Maybe 25 taught 32 how to crochet a sweater with a gerbil emblem on it. Maybe 32 and 25 stared into each others’ eyes for hours and vowed to never leave each other’s sides. Maybe 25 and 32 went to a Carpenter’s concert and heard “Close to You” sung live by Karen Carpenter and never were the same (it was the early 1970’s). We don’t know, we just know they interacted outside of the club.

Now I’ve never been a member of a karate club. I took karate classes at the local suburban recreation center with about 40 other 7 year-olds back in 1986 in the hopes that I could learn to crane kick like Ralph Macchio. That did not happen, and I never even made it to the white belt level. Instead I learned how reluctant a karate instructor can be to clean up a gym floor when a child (not me) pees in fear/boredom. So my karate knowledge is pretty much limited to the aforementioned 1980’s film franchise and Miss Piggy.

Back to the actual karate club at hand. As I mentioned, I have never had the experience of being involved in a karate club, but if Zachary’s example is representative of all karate clubs, they are dens of backstabbing and DRAMA. You see, there were two individuals in the club who had very different ideas of how the club should run. The karate instructor felt that karate club fees should be raised, and the club president wanted to keep the fees low. These two didn’t just disagree with each other and then go around karate chopping as per usual. Instead things got heated. They each tried to recruit members of the club to be on their side. Alliances were forged and torn asunder. Names were called. People were karate chopped in the heart. Or not, I wasn’t born yet. Eventually the group split in two.

Now that you know the embellished karate club backstory, here’s a little challenge for you :

1.) Identify the two ring-leaders of the karate club discord of 1972.

2.) Identify two groups that correspond with how the group split.

Answers below:

First here are the ringleaders sowing the seeds of animosity in a once peaceful karate club:

The karate instructor is labelled 1, and the administrator is labelled 34. Knowing that, and without scrolling down, see if you could guess how this network was split. I have placed some highly realistic karate images below so you have to scroll down to find the answer.

Without any further delay, or high-kicking pork here’s the answer. Those in yellow sided with the administrator (34) and those in blue sided with the instructor (1):

How did that match up with your guesses?

It turns out this social network example is pretty famous. In fact there is a “Zachary’s Karate Club Club” that is made up of the first person at a social network conference who use this data set in their presentation. It even has its own tumblr! #socialnetworkgoals. The reason why this example is so famous is that it brings up a lot of interesting questions including:

1.) What is the best way to visualize this network? Is there an algorithm that can quickly create that visualization?

2.) What makes a network visualization “good”?

3.) What is the best way to identify influential members of a network?

4.) How can we detect sub-groups in a network?

On top of that, this is a nice small example of a network that has many common features of social networks. I have used this example in one paper already, and am working on including it in another paper about a really different application. If you want to get started with networks, go ahead and download the data set, fire up R, and try out the SNA and igraph packages. Lastly, don’t forget to cite the original paper:

W. W. Zachary, An information flow model for conflict and fission in small groups, Journal of Anthropological Research 33, 452-473 (1977).

Happy social networking! May you one day join Zachary’s Karate Club Club!